I know this is a PbtA thread, but what are the differences in Forged in the Dark?
There are a lot of specific differences, and just as PbtA games can be very different from one another, there's a lot of variety among FitD games.
But imo the biggest difference is that in FitD when the player gets a consequence, they can choose to resist it, usually by adding a variable amount of Stress points. Resisting might totally negate a consequence (the guard didn't see you sneaking around) or reduce it (the guard isn't raising the alarm, but they are coming to investigate).
Once your Stress track is full, you take a Trauma, typically meaning you're basically out of the session. Traumas are different from physical injuries, in that they usually can't be removed, they have lingering effects (you're paranoid, etc.) and if you get four of them, your character is retired.
Though Traumas are usually permanent, Stress is removed by doing something in downtime (play alternates between a score/mission phase, and then a downtime phase), like indulging in a Vice.
The PCs' ability to resist--at least until they're full on Stress--means GMs are maybe encouraged to move harder against them than in PbtA (if you're familiar with Brindlewood Bay or The Between, resisting is a little like putting on a Crown or Mask). Other stuff gets generated and accelerated, too. Gaining Stress through resisting consequences feeds into downtime activities and the narrative consequences those can generate. And the Traumas that result from running out of Stress are another kind of existential threat, in addition to whether you live or die. Also, in theory, racking up Traumas makes you more and more of a weirdo, which is fun to play. Resisting consequences isn't the only way to accrue Stress and start related things rolling, but it's a consistent one.
Another big difference is that FitD games tend to be more specific about the stakes of each dice roll. Based on the fictional positioning, including what the PC is trying to do, the GM might say that what a PC is doing is a
risky action that will have
limited effect (firing a slew of wild shots at approaching enemies while you run for cover, hoping to rattle them or keep their heads down for a moment) or it's a
desperate action with
moderate effect (you're standing your ground, gunslinger-style, and trying to drop as many as you can). A lot of stuff might factor into how dangerous or effective the action is, like how many enemies there are, whether they have armor, what kind of weapon you're using, etc. I'm probably making it sound more complicated than it is, but to me it offers a bit more structure to a given action than in PbtA, and that has its benefits and drawbacks.
I'm personally way more comfortable with FitD's generally more structured (but still very very open-ended) approach than with PbtA, because I'm still a trad little baby at heart. But they share a lot, especially the common dice roll result of success-with-consequence, and the overall emphasis on consequences driving the entire play loop, instead of constant GM prep.